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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Modeling of electrostatic gate operations in the Kane solid state quantum computer

Chris I. Pakes, Cameron J. Wellard, David N. Jamieson, Lloyd C. L. Hollenberg, Steven Prawer, Andrew S. Dzurak, A. R. Hamilton, Robert G. Clark

Published Nov 21, 2001• 1 citation
Publisher

Abstract

The nuclear spin quantum computer proposed by Kane1 exploits as a qubit array 31P dopants embedded within a silicon matrix. Single-qubit operations are controlled by the application of electrostatic potentials via a set of metallic A gates, situated above the donors, on the silicon surface, that tune the resonance frequency of individual nuclear spins, and a globally applied RF magnetic field that flips spins at resonance. Coupling between qubits is controlled by the application of potentials via a set of J gates, between the donors, that induce an electron-mediated coupling between nuclear spins. We report the results of a study of the electric field and potential profiles arising within the Kane device from typical gate operations. The extent to which a single nuclear spin can be tuned independently of its neighbours, by operation of an associated A-gate, is examined and key design parameters in the Kane architecture are addressed. Implications for current fabrication strategies involving the implantation of 31P atoms are discussed. Solution of the Poisson equation has been carried out by simulation using a TCAD modeling package (Integrated Systems Engineering AG).

DOI
10.1117/12.449136

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Device modelling for the Kane quantum computer architecture : solution of the donor electron Schrodinger equation

Louise Olsen‐Kettle

In the Kane silicon-based electron-mediated nuclear spin quantum computer architecture, phosphorous is doped at precise positions in a silicon lattice, and the P donor nuclear spins act as qubits. Logical operations on the nuclear spins are performed using externally applied magnetic and electric fields. There are two important interactions: the hyperfine and exchange interactions, crucial for logical qubit operations. Single qubit operations are performed by applying radio frequency magnetic fields resonant with targeted nuclear spin transition frequencies, tuned by the gate-controlled hyperfine interaction. Two qubit operations are mediated through the exchange interaction between adjacent donor electrons. It is important to examine how these two interactions vary as functions of experimental parameters. Here we provide such an investigation. First, we examine the effects of varying several experimental parameters: gate voltage, inter donor separation, donor depth below the silicon oxide interface and back gate depth, to explore how these variables affect the donor electro density. Second, we calculate the hyperfine interaction and the exchange coupling as a function of these parameters. These calculations were performed using an anisotropic effective mass Hamiltonian. The electric field potential was obtained using Technology Computer Aided Design software, and the interfaces were modelled as a barrier using a step function. We aim to provide relevant information for the experimental design of these devices and highlight the significance of environmental factors other than gate potential that affect the donor electron.

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Single-qubit operations on the Kane quantum computer

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In this paper we investigate the implementation of single-qubit operations in the Kane solid-state quantum computer by Rabi flipping the nuclear qubits via the application of resonant radio-frequency fields. Specifically, we calculate the change in the resonance frequency of the nuclear qubits with the application of electric potentials to metallic control gates designed to address individual qubits, as well as the effects these fields have on neighbouring qubits. We find that although the resonance frequencies of the neighbouring qubits are shifted, it is still theoretically possible to implement single-qubit operations with the fidelity required for large-scale quantum computation using this technique.

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Modelling single-electron-transistor-based readout in the Kane solid-state quantum computer

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The Kane (Kane B E 1998 Nature 393 133) solid-state quantum computer aims to exploit as qubits an array of 31 P nuclear spins embedded in a silicon matrix. A proposed scheme for readout of a qubit spin state relies on measurement of the associated spin state of its donor electron, by attempting to induce and detect, using a single-electron transistor (SET), spin-polarized motion of the electron to an adjacent donor site. The sensitivity required of a SET for detection of sub-surface electronic charge motion in a MOS architecture is examined by simulation of the capacitive coupling of the buried charge to the SET device. It is shown that the SET can support readout of the qubit electronic charge states within the appropriate electron spin relaxation time. This paper presents a novel application of Technology Computer Aided Design, which presents itself as a valuable tool for the design of nanoscale device architectures employing precision electrometry for readout of quantum logic states.

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Spin is a quantum mechanical property that describes the magnetic orientation of elementary and composite particles such as electrons and nuclei. For spin-half particles placed in a magnetic field, two states with differing energies are defined. Proposals exist for developing a revolutionary kind of computer that encodes bits of information on the states of a simple quantum two-level system - like those of a spin in a magnetic field. These quantum computers exploit the fundamental principles of quantum mechanics in order to perform certain calculations exponentially faster than their classical counterparts. Key to the development of such a device is the identification of potential systems that are suitable for employment as a quantum bit (qubit). This thesis explores quantum bits constructed from the spin states of single atoms hosted in silicon semiconductor devices. Silicon is an exceptional platform for spin-based quantum computing - in addition to being the dominant material in the microelectronic industry, it is also predominantly composed of nuclear spin-zero isotopes, providing very little background magnetic disturbance. The donor-atom phosphorus (31P) is investigated here. It possesses a nucleus that binds an additional electron to its positive charge, providing two distinct spin qubits. Here, several world-first experimental milestones in spin-based quantum information processing are reported. First, the readout of the electron spin is demonstrated in single-shot, using a silicon device which combines implanted phosphorus donors with a sensitive nanoscale electrometer. Then, the electron spin is coherently operated as a qubit by delivering on-chip microwave excitations. Combining the electron spin detection and control capabilities enables a quantum non-demolition measurement of the single 31P nuclear spin. Experiments yield exceptional nuclear readout fidelities - the highest for any solid-state qubit. Through an application of nuclear magnetic resonance, high-fidelity quantum control of the nuclear spin qubit is demonstrated. Finally, a single spin-bearing silicon nucleus (29Si) coupled to the electron spin is detected in single-shot and operated as a qubit. These results, along with the clear pathways identified for improving device performance, illustrate that single-atom electron and nuclear spin qubits in silicon constitute an excellent basis on which to construct a quantum computer.

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A silicon-based cluster state quantum computer

John J. L. Morton

It has been over ten years since Kane's influential proposal for a silicon-based nuclear spin quantum computer using phosphorous donors. Since then, silicon-based architectures have been refined as the experimental challenges associated with the original proposal have become better understood, while simultaneously a number of powerful and generic models for quantum computation have emerged. Here, I discuss how the cluster state or "one-way" model for quantum computing might be advantageously applied to donors in silicon, with the potential to substantially reduce the practical requirements of a successful implementation. The essence of the scheme is to use the electron spin associated with a donor to weave an entangled network between 31P donor nuclear spins. This resource has been shown to have exceptional coherence times and supports universal quantum computation through local measurements on the nuclear spins. Some of the key ingredients, such as global spin manipulation, have been robustly established, while others, such as single spin measurement, have seen much progress in recent years. A key challenge will be the demonstration of electron transfer between donors that preserves spin coherence.

arXiv:0905.4008•May 25, 2009•10 citations
The nuclear spin quantum computer proposed by Kane1 exploits as a qubit array 31P dopants embedded within a silicon matrix. Single-qubit operations are controlled by the application of electrostatic potentials via a set of metallic A gates, situated above the donors, on the silicon surface, that tune the resonance frequency of individual nuclear spins, and a globally applied RF magnetic field that flips spins at resonance. Coupling between qubits is controlled by the application of potentials via a set of J gates, between the donors, that induce an electron-mediated coupling between nuclear spins. We report the results of a study of the electric field and potential profiles arising within the Kane device from typical gate operations. The extent to which a single nuclear spin can be tuned independently of its neighbours, by operation of an associated A-gate, is examined and key design parameters in the Kane architecture are addressed. Implications for current fabrication strategies involving the implantation of 31P atoms are discussed. Solution of the Poisson equation has been carried out by simulation using a TCAD modeling package (Integrated Systems Engineering AG).
In the Kane silicon-based electron-mediated nuclear spin quantum computer architecture, phosphorous is doped at precise positions in a silicon lattice, and the P donor nuclear spins act as qubits. Logical operations on the nuclear spins are performed using externally applied magnetic and electric fields. There are two important interactions: the hyperfine and exchange interactions, crucial for logical qubit operations. Single qubit operations are performed by applying radio frequency magnetic fields resonant with targeted nuclear spin transition frequencies, tuned by the gate-controlled hyperfine interaction. Two qubit operations are mediated through the exchange interaction between adjacent donor electrons. It is important to examine how these two interactions vary as functions of experimental parameters. Here we provide such an investigation. First, we examine the effects of varying several experimental parameters: gate voltage, inter donor separation, donor depth below the silicon oxide interface and back gate depth, to explore how these variables affect the donor electro density. Second, we calculate the hyperfine interaction and the exchange coupling as a function of these parameters. These calculations were performed using an anisotropic effective mass Hamiltonian. The electric field potential was obtained using Technology Computer Aided Design software, and the interfaces were modelled as a barrier using a step function. We aim to provide relevant information for the experimental design of these devices and highlight the significance of environmental factors other than gate potential that affect the donor electron.
In this paper we investigate the implementation of single-qubit operations in the Kane solid-state quantum computer by Rabi flipping the nuclear qubits via the application of resonant radio-frequency fields. Specifically, we calculate the change in the resonance frequency of the nuclear qubits with the application of electric potentials to metallic control gates designed to address individual qubits, as well as the effects these fields have on neighbouring qubits. We find that although the resonance frequencies of the neighbouring qubits are shifted, it is still theoretically possible to implement single-qubit operations with the fidelity required for large-scale quantum computation using this technique.
The Kane (Kane B E 1998 Nature 393 133) solid-state quantum computer aims to exploit as qubits an array of 31 P nuclear spins embedded in a silicon matrix. A proposed scheme for readout of a qubit spin state relies on measurement of the associated spin state of its donor electron, by attempting to induce and detect, using a single-electron transistor (SET), spin-polarized motion of the electron to an adjacent donor site. The sensitivity required of a SET for detection of sub-surface electronic charge motion in a MOS architecture is examined by simulation of the capacitive coupling of the buried charge to the SET device. It is shown that the SET can support readout of the qubit electronic charge states within the appropriate electron spin relaxation time. This paper presents a novel application of Technology Computer Aided Design, which presents itself as a valuable tool for the design of nanoscale device architectures employing precision electrometry for readout of quantum logic states.
The spins of atoms and atom-like systems are among the most coherent objects in which to store quantum information. However, the need to address them using oscillating magnetic fields hinders their integration with quantum electronic devices. Here, we circumvent this hurdle by operating a single-atom "flip-flop" qubit in silicon, where quantum information is encoded in the electron-nuclear states of a phosphorus donor. The qubit is controlled using local electric fields at microwave frequencies, produced within a metal-oxide-semiconductor device. The electrical drive is mediated by the modulation of the electron-nuclear hyperfine coupling, a method that can be extended to many other atomic and molecular systems and to the hyperpolarization of nuclear spin ensembles. These results pave the way to the construction of solid-state quantum processors where dense arrays of atoms can be controlled using only local electric fields.
Spin is a quantum mechanical property that describes the magnetic orientation of elementary and composite particles such as electrons and nuclei. For spin-half particles placed in a magnetic field, two states with differing energies are defined. Proposals exist for developing a revolutionary kind of computer that encodes bits of information on the states of a simple quantum two-level system - like those of a spin in a magnetic field. These quantum computers exploit the fundamental principles of quantum mechanics in order to perform certain calculations exponentially faster than their classical counterparts. Key to the development of such a device is the identification of potential systems that are suitable for employment as a quantum bit (qubit). This thesis explores quantum bits constructed from the spin states of single atoms hosted in silicon semiconductor devices. Silicon is an exceptional platform for spin-based quantum computing - in addition to being the dominant material in the microelectronic industry, it is also predominantly composed of nuclear spin-zero isotopes, providing very little background magnetic disturbance. The donor-atom phosphorus (31P) is investigated here. It possesses a nucleus that binds an additional electron to its positive charge, providing two distinct spin qubits. Here, several world-first experimental milestones in spin-based quantum information processing are reported. First, the readout of the electron spin is demonstrated in single-shot, using a silicon device which combines implanted phosphorus donors with a sensitive nanoscale electrometer. Then, the electron spin is coherently operated as a qubit by delivering on-chip microwave excitations. Combining the electron spin detection and control capabilities enables a quantum non-demolition measurement of the single 31P nuclear spin. Experiments yield exceptional nuclear readout fidelities - the highest for any solid-state qubit. Through an application of nuclear magnetic resonance, high-fidelity quantum control of the nuclear spin qubit is demonstrated. Finally, a single spin-bearing silicon nucleus (29Si) coupled to the electron spin is detected in single-shot and operated as a qubit. These results, along with the clear pathways identified for improving device performance, illustrate that single-atom electron and nuclear spin qubits in silicon constitute an excellent basis on which to construct a quantum computer.
It has been over ten years since Kane's influential proposal for a silicon-based nuclear spin quantum computer using phosphorous donors. Since then, silicon-based architectures have been refined as the experimental challenges associated with the original proposal have become better understood, while simultaneously a number of powerful and generic models for quantum computation have emerged. Here, I discuss how the cluster state or "one-way" model for quantum computing might be advantageously applied to donors in silicon, with the potential to substantially reduce the practical requirements of a successful implementation. The essence of the scheme is to use the electron spin associated with a donor to weave an entangled network between 31P donor nuclear spins. This resource has been shown to have exceptional coherence times and supports universal quantum computation through local measurements on the nuclear spins. Some of the key ingredients, such as global spin manipulation, have been robustly established, while others, such as single spin measurement, have seen much progress in recent years. A key challenge will be the demonstration of electron transfer between donors that preserves spin coherence.